1. Game Trees and Minimax Algorithm
J.-S. Roger Jang (張智星)
MIR Lab, CSIE Dept.
National Taiwan University
2019/5/24

2. Game trees Game trees Minimax algorithm a-b pruning
A tree to represent the progression of states during a two-player game
Minimax algorithm
A way of finding an optimal move in a two-player game (or in a game tree)
a-b pruning
A way of speeding up minimax algorithm

3. MinMax Rule: Game Tree of Tic-Tac-Toc
O’s move!
1: O wins
0: Draw
-1: O loses X X O
Max O X O -1 -1
X’s move! X X O X X O X X O
Min O O O O O X O X O O X O 1 -1 -1 1 X X O X X O X X O X X O X X O X X O
Max O O X O O X O O X X O O O O X O X O X X O O X O O X O X O X 1 1 X X O X X O X X O X X O
Min O O X O O O O O X O O O X O O X O X X O O X O X

4. Example: a-b Pruning in a Game Tree (1/3)
Source
Max
Min
Max
Min 8 7 3 9 9 8 2 4 1 8 8 9 9 9 3 4

5. Example: a-b Pruning in a Game Tree (2/3)
Source
Stey-by-step DFS!
Max
Min
Max
Min 3 17 2 12 15 25 2 5 3 2 14

6. Example: a-b Pruning in a Game Tree (3/3)
Source

7. Exercise 1: a-b Pruning in a Game Tree
Display how the search can be reduced via a-b Pruning
Max
Min
Max
Min 5 7 3 9 6 5 2 4 1 8 1 6 4 9 3 4

8. Exercise 2: a-b Pruning in a Game Tree
Display how the search can be reduced via a-b Pruning
Max
Min
Max
Min 8 7 3 9 2 5 5 4 1 8 6 1 4 9 3 4